Written Assignment 2
Math 100 Fall 2013
Due: Friday, October 18
Total: 100 points
1. (12 pts) Compute the following limits
(a) lim
x+
x
(b) lim cos e(
3
x
x
x+sin x)
x
(c) lim cos e(
3
x+sin x)
x
2. (10 pts) Let f (x) =
x2 +1
.
x+1
Find f (x) using only t
Written Assignment 1
Math 100 Fall 2013
Due: Friday, September 27
Total: 100 points
1. (10 pts) Solve the given inequality, and illustrate the solution set on the real line.
(a) x2 (x2 1)(x + 1)(x + 3) (x2 1)(3x 2)(x + 1)(x + 3)
Solution:
The inequality x
Math 100, Fall 2013
Homework 4
Due : Friday, November 29, 2013
Exercise 1.(6 marks) Show that ln(x + 1) < x for all x > 0.
Hint : Consider the function F (x) = ln(1 + x) x.
Exercise 2.(12 marks) Evaluate the following limits.
(i)
(ii)
(iii)
(iv)
ln(sin r)
Written Assignment 1
Math 100 Fall 2013
Due: Friday, September 27
Total: 100 points
1. (10 pts) Solve the given inequality, and illustrate the solution set on the real line.
(a) x2 (x2 1)(x + 1)(x + 3) (x2 1)(3x 2)(x + 1)(x + 3)
(b) 2x < 3x + 4 2x2 + 5x
2